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영과잉 회귀모형에 대한 베이지안 분석

Bayesian Analysis for the Zero-inflated Regression Models

  • 장학진 (한양대학교 응용수학과) ;
  • 강윤회 (한양대학교 응용수학과) ;
  • 이수범 (서울시립대학교 교통공학과) ;
  • 김성욱 (한양대학교 응용수학과)
  • Jang, Hak-Jin (Division of Applied Mathematics, Hanyang University) ;
  • Kang, Yun-Hee (Division of Applied Mathematics, Hanyang University) ;
  • Lee, S. (Division of Transportation Engineering, The University of SEOUL) ;
  • Kim, Seong-W. (Division of Applied Mathematics, Hanyang University)
  • 발행 : 2008.08.31

초록

셀 수 있는 이산 자료 중에서 일반적인 모형에 비하여 영의 빈도가 과도하게 많이 관측되는 자료가 있다. 이러한 경우에 포아송 또는 음이항회귀모형과 같은 일반적인 회귀모형에 의한 분석은 적절하지 못하다. 본 논문에서는 영과잉 포아송회귀모형과 영과잉 음이항회귀모형에 대하여 베이지안 분석을 하였다. 또한, 마코브 연쇄 몬테카롤로 방법으로 계산한 베이즈 요인을 이용하여 모형선택을 하였다. 실제 교통사고 자료를 분석하여 이론적인 결과들을 뒷받침하였다.

We often encounter the situation that discrete count data have a large portion of zeros. In this case, it is not appropriate to analyze the data based on standard regression models such as the poisson or negative binomial regression models. In this article, we consider Bayesian analysis for two commonly used models. They are zero-inflated poisson and negative binomial regression models. We use the Bayes factor as a model selection tool and computation is proceeded via Markov chain Monte Carlo methods. Crash count data are analyzed to support theoretical results.

키워드

참고문헌

  1. 임아경, 오만숙 (2006). 영과잉 포아송 회귀모형에 대한 베이지안 추론: 구강위생 자료에의 적용, <응용통계연구>, 19, 505-519 https://doi.org/10.5351/KJAS.2006.19.3.505
  2. Gelfand, A. E. and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities, Journal of the America Statistical Association, 85, 389-409
  3. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741 https://doi.org/10.1109/TPAMI.1984.4767596
  4. Jeffreys, H. (1961). Theory of Probability, (Third edition), Oxford University Press, Oxford
  5. Joshua, S. C. and Garber, N. J. (1990). Estimating truck accident rate and involvements using linear and poisson regression models, Transportation Planning and Technology, 15, 41-58 https://doi.org/10.1080/03081069008717439
  6. Jovanis, P. P. and Chang, H. L. (1986). Modelling the relationship of accidents to miles traveled, Transportation Research Record, 1068, 42-51
  7. McCulloch, R. and Rossi, P. E. (1991). A bayesian approach to testing the arbitrage pricing theory, Journal of Econometrics, 49, 141-168 https://doi.org/10.1016/0304-4076(91)90012-3
  8. Miaou, S. P. and Lum, H. (1993). Modeling vehicle accidents and highway geometric design relationships, Accident Analysis and Prevention, 25, 689-709 https://doi.org/10.1016/0001-4575(93)90034-T
  9. Milton, J. C. and Mannering, F. L. (1998). The relationship among highway geometrics, traffic-related elements and motor-vehicle accident frequencies, Transportation, 25, 395-413 https://doi.org/10.1023/A:1005095725001
  10. Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap, Journal of the Royal Statistical Society, Series B, 56, 3-48
  11. Poch, M. and Mannering, F. (1996). Negative binomial analysis of intersection-accident frequencies, Journal of Transportation Engineering, 122, 105-113 https://doi.org/10.1061/(ASCE)0733-947X(1996)122:2(105)
  12. Raftery, A. E. and Banfield, J. D. (1991). Stopping the Gibbs Sampler, the use of morphology and other issues in spatial statistics, Annals of the Institute of Statistical Mathematics, 43, 32-43
  13. Shankar, V., Mannering, F. L. and Barfield, W. (1995). Effect of roadway geometrics and environmental factors on rural freeway accident frequencies. Accident Analysis and Prevention, 27, 371-389 https://doi.org/10.1016/0001-4575(94)00078-Z
  14. Shankar, V., Milton, J. C. and Mannering, F. L. (1997). Modeling accident frequencies as zero-altered probability process: An empirical inquiry, Accident Analysis and Prevention, 29, 829-837 https://doi.org/10.1016/S0001-4575(97)00052-3
  15. Szabo, R. M. and Khoshgoftaar, T. M. (2000). Exploring a poisson regression fault model: A comparative study, Technical Report TR-CSE-00-56, Florida Atlantic University

피인용 문헌

  1. Development of safety performance functions and crash modification factors for expressway ramps 2017, https://doi.org/10.1007/s12205-017-0582-1
  2. Bayesian Inference for the Zero In ated Negative Binomial Regression Model vol.24, pp.5, 2011, https://doi.org/10.5351/KJAS.2011.24.5.951